View in EDS

Identifying a control function in parabolic partial differential equations from overspecified boundary data

Saved in:
Bibliographic Details
Title: Identifying a control function in parabolic partial differential equations from overspecified boundary data
Authors: Tatari, Mehdi1 mehditatari@aut.ac.ir, Dehghan, Mehdi mdehghan@aut.ac.ir
Source: Computers & Mathematics with Applications. Jun2007, Vol. 53 Issue 12, p1933-1942. 10p.
Subjects: Mathematical functions, Parabolic differential equations, Boundary value problems, Decomposition method, Differential equations, Quasilinearization
Abstract: Abstract: Determination of an unknown time-dependent function in parabolic partial differential equations, plays a very important role in many branches of science and engineering. In the current investigation, the Adomian decomposition method is used for finding a control parameter in the quasilinear parabolic equation , in with known initial and boundary conditions and subject to an additional condition in the form of which is called the boundary integral overspecification. The main approach is to change this inverse problem to a direct problem and then solve the resulting equation using the well known Adomian decomposition method. The decomposition procedure of Adomian provides the solution in a rapidly convergent series where the series may lead to the solution in a closed form. Furthermore due to the rapid convergence of Adomian’s method, a truncation of the series solution with sufficiently large number of implemented components can be considered as an accurate approximation of the exact solution. This method provides a reliable algorithm that requires less work if compared with the traditional techniques. Some illustrative examples are presented to show the efficiency of the presented method. [Copyright &y& Elsevier]
Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Description
Abstract:Abstract: Determination of an unknown time-dependent function in parabolic partial differential equations, plays a very important role in many branches of science and engineering. In the current investigation, the Adomian decomposition method is used for finding a control parameter in the quasilinear parabolic equation , in with known initial and boundary conditions and subject to an additional condition in the form of which is called the boundary integral overspecification. The main approach is to change this inverse problem to a direct problem and then solve the resulting equation using the well known Adomian decomposition method. The decomposition procedure of Adomian provides the solution in a rapidly convergent series where the series may lead to the solution in a closed form. Furthermore due to the rapid convergence of Adomian’s method, a truncation of the series solution with sufficiently large number of implemented components can be considered as an accurate approximation of the exact solution. This method provides a reliable algorithm that requires less work if compared with the traditional techniques. Some illustrative examples are presented to show the efficiency of the presented method. [Copyright &y& Elsevier]
ISSN:08981221
DOI:10.1016/j.camwa.2006.01.018